ON MOTION OF CHARGED PARTICLES IN A SELF-CONSISTENT STANDING POTENTIAL WAVE

This paper deals with an asymptotic solution of the equations of Vlasov and Poisson describing one-dimensional plasma motion. The self-consistent, non-external, potential is in lowest order a standing wave. The solution involves expansions in the wave amplitude. Higher order coefficients of the potential series are expressed in terms of the distribution function, which is a function of one constant of motion only, obtained by integrating once the equation of motion. The omission of a second integration, and the associated constant of motion, amounts to an assumption of random phases. The wave is shown to be stable. © 1969.